Original Article
225
Development of QSAR for Antimicrobial Activity of Substituted Benzimidazoles
Authors
N. Vashist1, S. S. Sambi1, P. Kumar2, B. Narasimhan2
Affiliations
1
2
Key words ▶ Benzimidazoles ● ▶ Antimicrobial activity ● ▶ QSAR ●
Abstract
▼
QSAR analysis has been done to correlate antimicrobial activity of substituted benzimidazole derivatives with their physicochemical parameters. Developed QSAR models have been cross validated using leave one out (LOO) method. Statistical parameters like probable error of
Introduction
▼
received 30.10.2013 accepted 07.11.2013 Bibliography DOI http://dx.doi.org/ 10.1055/s-0034-1371828 Published online: January 21, 2015 Drug Res 2015; 65: 225–230 © Georg Thieme Verlag KG Stuttgart · New York ISSN 2194-9379 Correspondence Dr. B. Narasimhan Faculty of Pharmaceutical Sciences Maharshi Dayanand University Delhi Road Rohtak-124001 India Tel.: + 91/941/6649 342 Fax: + 91/1262/274 133 [email protected]
In recent years, a number of life-threatening infections caused by multi-drug resistant Gram-positive and Gram-negative pathogenic bacteria have reached an alarming level in many countries. Infections caused by these microorganisms pose a serious challenge to the medical community to develop an effective therapy by developing novel antibacterial agents [1]. The benzimidazole moiety is an important pharmacophore in medicinal chemistry. Diverse biological activities and clinical applications such as antimicrobial [2], anticancer [3] activities have been reported for these derivatives. Quantitative Structure Activity Relationship (QSAR) has proved to be a useful tool for rational search of bioactive molecules. This eliminates unnecessary synthesis of many structures even without testing those [4]. Our research work devoted to rational drug design [5] established the importance of this analytical approach. Hence, in the present study, we hereby report the QSAR studies for substituted benzimidazoles reported by Selvam et al. and Tuncbilek et al. [6, 7].
Results and Discussion
▼
The present study was designed to develop quantitative model to predict the correlation between the antimicrobial activity of a dataset of 45 benzimidazole derivatives against E. coli, S. aureus and ▶ Table 1) and the structural descripC. albicans ( ●
the coefficient of correlation (PE), least square error (LSE), Friedman’s lack of fit measure (LOF), standard error of prediction (SEP) and quality value (Q) were also used to cross validate the models. QSAR studies established the importance of WAP, Mlog P and UI in describing the antimicrobial activities of substituted benzimidazole derivatives.
tors using MLR analysis. Numerical values of various descriptors calculated by Dragon software programme [8] are given in ● ▶ Table 2. Out of these 45 derivatives, some of the compounds having activity against E. coli (1, 2, 4, 10, 12, 28, 33, 36–39, 42 and 45), S. aureus (16, 18– 23, 29–32, 34, 35, 38, 39, 41 and 43), and C. albicans (3, 5, 10, 15, 16, 18, 19, 21, 23, 25–27, 29, 32, 40, 43 and 45) were identified as outliers and removed before the development of best QSAR models as per results of our previous studies [5]. QSAR model for explaining antimicrobial activity of benzimidazole derivatives against E. coli (Eq. 1) was developed using WAP.
QSAR model for antibacterial activity of benzimidazole derivatives against E. coli pMICec = 0.0000146 WAP + 0.669
(1)
n = 31, r = 0.964, r2 = 0.929, Se = 0.0626, q2 = 0.929, F = 379.029, PE = 0.0085, LSE = 0.114, LOF = 0.130, SEP = 0.011, VIF = 0.071, Q = 15.30 Here and thereafter, n is the number of data points, r is the correlation coefficient; r2 is the squared correlation coefficient, Se is the standard error of the estimate; q2 is the cross validated r2 which is obtained by leave one out (LOO) method, F, is the Fischer ratio, PE is probable error of the coefficient of correlation, LSE is least square error, LOF is Friedman’s lack of fit measure, SEP is standard error of prediction, VIF is the variation inflation factor and Q is the quality value.
Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
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University School of Chemical Technology, Guru Gobind Singh Indraprastha University, New Delhi, India Faculty of Pharmaceutical Sciences, Maharshi Dayanand University, Rohtak, India
226 Original Article
Table 1 Antimicrobial activity of benzimidazole derivatives. N H
Comp.
R
1
NO
2
Cl
3
Comp.
OCH
R
6
NO
7
Cl
8
Comp.
OCH
R
11
NO
12
Cl
13
OCH
R
N
pMICec
pMICsa
pMICca
Comp.
1.256
1.212
1.388
4
1.375
1.030
1.266
5
1.153
1.173
1.153
pMICec
pMICsa
pMICca
Comp.
1.446
1.343
1.581
9
1.120
1.180
1.435
10
1.284
1.402
1.351
pMICec
pMICsa
pMICca
1.415
1.277
1.665
14
1.529
1.494
1.494
15
1.325
1.157
1.325
R4
Comp.
R
CH
R
CH
R
CH
pMICec
pMICsa
pMICca
1.305
1.121
1.536
1.016
1.002
1.192
pMICec
pMICsa
pMICca
1.344
1.118
1.301
1.509
1.191
1.174
pMICec
pMICsa
pMICca
1.666
1.342
1.579
1.264
1.081
1.188
Comp.
R1
R2
R3
pMICec
pMICsa
pMICca
16
Cl
H
H
0.645
0.645
0.645
17
Cl
Cl
H
0.708
1.611
1.310
18
Cl
Cl
Cl
0.763
1.968
0.763
19
Cl
Cl
NHCH(CH3)2
0.796
0.796
0.796
20
Cl
Cl
Br
0.825
2.030
1.126
21
Cl
Cl
NH2
0.733
1.937
1.636
22
Cl
H
NH2
0.673
0.974
0.974
23
Cl
OC2H5
0.856
1.759
0.856
0.875
0.875
1.176
0.887
0.887
1.791
F
24
Cl
OC2H5 Cl
25
Cl
OC2H5
NO
Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
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N
Original Article
227
Table 1 Antimicrobial Continued. activity of benzimidazole derivatives. Comp.
R1
R2
26
Cl
OC2H5
27
Cl
Cl
R3
R4
pMICec
pMICsa
pMICca
0.902
0.902
1.805
0.859
1.160
1.762
1.192
0.891
1.493
H
0.750
1.955
1.653
H
0.775
1.979
1.377
OCOCH
OCH
28
Cl
Cl OCOCH
29
Cl
Cl
30
Cl
Cl
31
Cl
Cl
H
0.805
2.010
1.407
32
Cl
Cl
H
0.797
0.797
1.098
33
Cl
Cl
1.145
1.145
1.145
0.864
0.864
1.466
F
Cl
34
Cl
Cl
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F
Cl
35
Cl
Cl
0.889
1.792
1.190
36
Cl
Cl
0.882
0.882
1.484
37
Cl
H
1.100
1.401
1.401
1.122
0.821
1.122
F
38
Cl
H Cl
39
Cl
H
0.906
2.111
1.207
40
Cl
H
0.851
0.851
0.851
41
Cl
H
0.835
0.835
1.437
42
Cl
H
1.150
0.849
1.451
43
Cl
H
0.809
0.809
1.712
0.832
1.434
1.434
0.841
1.142
1.744
OCOCH
NO
CN
44
Cl
H N(CH )
45
Cl
H
The developed QSAR model (Eq. 1) was cross validated by q2 value obtained by leave one out (LOO) method. The higher value of q2 (0.929) indicated that the model developed is a valid one. As the observed and predicted values are close to each other ▶ Table 3), the QSAR model for antibacterial activity against ( ● E. coli (Eq. 1) is a valid one [9]. The validity of the developed QSAR model was also supported by other statistical parameters such as low value of LSE, LOF, PE and the high Q values favours the validity of developed QSAR model (Eq. 1).
QSAR model for antibacterial activity of benzimidazole derivatives against S. aureus
Mlog P was found to be the most important descriptor for explaining the antibacterial activity of benzimidazole derivatives against S. aureus. pMICsa = − 0.114 Mlog P + 1.666
(2)
n = 28, r = 0.364, r2 = 0.132, Se = 0.200, q2 = 0.133, F = 3.969, PE = 0.109, LSE = 0.509, LOF = 0.862, SEP = 0.025, VIF = 0.868, Q = 1.82 Coupling of Mlog P with WAP and 1χsol lead to best MLR model against S. aureus having improved r (from 0.364 to 0.751) and q2 (from 0.132 to 0.564) values (Eq. 3). Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
228 Original Article
Comp.
ZM1
ZM2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
138.00 128.00 132.00 138.00 128.00 168.00 158.00 162.00 168.00 158.00 166.00 156.00 160.00 166.00 156.00 82.00 88.00 94.00 108.00 94.00 94.00 88.00 136.00 136.00 146.00 150.00 132.00 142.00 98.00 98.00 116.00 118.00 128.00 128.00 146.00 148.00 122.00 122.00 158.00 136.00 132.00 140.00 126.00 132.00 142.00
161.00 149.00 154.00 162.00 149.00 205.00 193.00 198.00 206.00 193.00 200.00 188.00 193.00 201.00 188.00 98.00 106.00 114.00 129.00 114.00 114.00 106.00 164.00 164.00 176.00 179.00 160.00 170.00 116.00 116.00 137.00 143.00 155.00 155.00 176.00 182.00 147.00 147.00 188.00 162.00 159.00 168.00 152.00 159.00 174.00
WAP 21 302.00 16 846.00 19 073.00 21 168.00 16 846.00 48 084.00 38 472.00 43 277.00 47 794.00 38 472.00 49 524.00 39 624.00 44 573.00 49 234.00 39 624.00 3 078.00 3 584.00 4 030.00 5 697.00 4 030.00 4 030.00 3 496.00 14 350.00 14 350.00 17 954.00 20 069.00 13 530.00 16 984.00 5 200.00 5 200.00 7 765.00 14 308.00 11 945.00 11 945.00 16 706.00 28 655.00 10 923.00 10 923.00 34 334.00 15 658.00 13 903.00 15 396.00 12 412.00 13 903.00 26 625.00
BAC 6.00 2.00 3.00 6.00 2.00 18.00 10.00 11.00 18.00 10.00 11.00 5.00 6.00 11.00 5.00 2.00 5.00 10.00 19.00 10.00 10.00 5.00 12.00 12.00 22.00 25.00 11.00 19.00 10.00 10.00 27.00 5.00 10.00 10.00 27.00 5.00 5.00 5.00 2.00 12.00 11.00 18.00 6.00 11.00 2.00
χ
1 v
χ
0χsol
1 sol
12.69 11.78 12.31 12.73 11.78 14.53 13.61 14.15 14.56 13.61 14.60 13.69 14.23 14.64 13.69 7.34 7.75 8.16 9.56 8.16 8.16 7.75 12.17 12.17 13.08 13.56 11.67 12.53 8.63 8.63 9.84 10.22 11.13 11.13 12.34 12.72 10.72 10.72 14.28 12.11 11.63 11.93 11.26 11.63 12.31
1
8.03 8.01 8.05 8.19 7.94 9.73 9.71 9.76 9.90 9.64 10.38 10.36 10.41 10.55 10.29 5.84 6.33 6.83 7.95 7.24 6.55 6.06 9.15 9.53 9.55 10.07 8.94 9.44 6.00 6.37 7.56 7.31 8.52 8.90 10.08 9.83 8.03 8.41 10.60 8.96 8.43 9.60 8.32 8.96 9.35
17.93 16.86 17.06 17.93 16.36 21.33 20.25 20.46 21.33 19.75 21.02 19.94 20.15 21.02 19.44 10.75 12.12 13.49 15.28 13.99 12.99 11.62 17.02 18.39 19.47 20.17 17.68 19.26 12.83 14.20 16.20 15.40 16.10 17.47 19.47 18.67 14.73 16.10 20.13 17.89 17.18 18.10 16.31 17.18 17.30
12.69 12.07 12.31 12.73 11.78 14.81 14.19 14.44 14.85 13.90 15.05 14.43 14.68 15.09 14.14 7.63 8.33 9.03 10.14 9.32 8.74 8.04 12.06 12.75 13.37 13.85 12.25 13.10 8.82 9.50 10.42 10.80 11.32 12.00 12.92 13.30 10.62 11.30 14.57 12.40 11.92 12.22 11.55 11.92 12.60
MLR QSAR model for antibacterial activity of benzimidazole derivatives against S. aureus
pMICsa = 0.0000212 WAP – 0.0667 Mlog P – 0.194 1χsol + 3.414 (3) n = 28, r = 0.751, r2 = 0.564, Se = 0.148, q2 = 0.564, F = 10.354, PE = 0.055, LSE = 0.509, LOF = 1.558, SEP = 0.025, VIF = 0.436, Q = 5.074 The higher value of q2 (0.564) indicated that the model developed is a valid one. Validity of the model also supported by the observed and predicted values of benzimidazole derivatives that ▶ Table 3). were found close to each other ( ●
Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
χ
UI 3.91 3.70 3.70 3.70 3.70 3.91 3.70 3.70 3.70 3.70 3.91 3.70 3.70 3.70 3.70 2.59 2.59 2.59 2.59 2.59 2.59 2.59 3.17 3.17 3.46 3.32 3.17 3.32 3.17 3.17 3.17 3.52 3.17 3.17 3.17 3.52 3.17 3.17 3.59 3.32 3.46 3.17 3.46 3.17 3.52
AMR
MlOGP
100.23 97.71 99.37 101.06 97.95 111.77 109.25 110.91 112.61 109.49 115.05 112.53 114.18 115.88 112.76 61.08 65.89 70.91 84.72 73.51 70.06 65.26 97.12 101.71 104.23 108.04 96.96 101.63 69.41 74.00 87.86 85.64 90.72 95.31 109.17 106.95 85.91 90.50 116.77 96.83 93.02 104.36 91.43 100.12 102.15
4.36 4.85 4.04 3.26 4.58 4.78 5.21 4.42 3.92 4.94 4.06 4.49 3.70 2.93 4.22 3.11 3.64 4.16 4.22 4.29 3.48 2.95 4.87 4.98 4.49 4.33 4.76 4.91 4.70 4.82 5.27 5.12 5.48 5.60 5.97 5.82 4.99 5.10 5.32 4.42 4.54 5.49 4.19 4.49 5.34
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Table 2 Values of selected molecular descriptors used in MLR analysis.
QSAR model for antifungal activity of benzimidazole derivatives against C. albicans
QSAR model for explaining antimicrobial activity of benzimidazole derivatives against C. albicans (Eq. 4) was developed using UI. pMICca = 0.0254 UI + 0.504
(4)
n = 28, r = 0.601, r2 = 0.362, Se = 0.133, q2 = 0.362, F = 14.735, PE = 0.080, LSE = 0.438, LOF = 0.508, SEP = 0.024, VIF = 0.638, Q = 2.721 In search of a better QSAR model for explaining antifungal activity of benzimidazole derivatives against C. albicans, we coupled UI with BAC, resulted in the best QSAR model (Eq. 5) having improved r and q2 values.
Original Article
229
Table 3 Comparison of observed verses predicted antimicrobial activity of benzimidazole derivatives using best MLR models.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
pMICsa
pMICec Obs.
Pred.
1.26 1.37 1.15 1.31 1.02 1.45 1.12 1.28 1.34 1.51 1.42 1.53 1.32 1.67 1.26 0.64 0.71 0.76 0.8 0.82 0.73 0.67 0.86 0.88 0.89 0.9 0.86 1.19 0.75 0.77 0.81 0.8 1.15 0.86 0.89 0.88 1.1 1.12 0.91 0.85 0.83 1.15 0.81 0.83 0.84
0.98 0.91 0.95 0.98 0.91 1.37 1.23 1.30 1.37 1.23 1.39 1.25 1.32 1.39 1.25 0.71 0.72 0.73 0.75 0.73 0.73 0.72 0.88 0.88 0.93 0.96 0.87 0.92 0.74 0.74 0.78 0.88 0.84 0.84 0.91 1.09 0.83 0.83 1.17 0.90 0.87 0.89 0.85 0.87 1.06
pMICca = 0.00456 BAC + 0.257 UI + 0.444
Res.
Obs.
0.28 0.46 0.20 0.33 0.11 0.08 − 0.11 − 0.02 − 0.03 0.28 0.03 0.28 0.00 0.28 0.01 − 0.07 − 0.01 0.03 0.05 0.09 0.00 − 0.05 − 0.02 0.00 − 0.04 − 0.06 − 0.01 0.27 0.01 0.03 0.03 − 0.08 0.31 0.02 − 0.02 − 0.21 0.27 0.29 − 0.26 − 0.05 − 0.04 0.26 − 0.04 − 0.04 − 0.22
1.21 1.03 1.17 1.12 1 1.34 1.18 1.4 1.12 1.19 1.28 1.49 1.16 1.34 1.08 0.64 1.61 1.97 0.8 2.03 1.94 0.97 1.76 0.88 0.89 0.9 1.16 0.89 1.95 1.98 2.01 0.8 1.15 0.86 1.79 0.88 1.4 0.82 2.11 0.85 0.83 0.85 0.81 1.43 1.14
(5)
n = 28, r = 0.629, r2 = 0.396, Se = 0.132, q2 = 0.393, F = 8.184, PE = 0.076, LSE = 0.438, LOF = 0.709, SEP = 0. 024, VIF = 0. 604, Q = 4.765 The developed QSAR model (Eq. 5) was cross validated by q2 value obtained by leave one out (LOO) method. The low value of q2 (0.396) indicated that the model developed is an invalid one. But according to the recommendations of Golbraikh and Tropsha, as the observed and predicted values are close to each other ▶ Table 3), the QSAR model for antifungal activity against C. ( ● albicans (Eq. 5) is a valid one [9]. The validity of the developed QSAR model was also supported by the low LSE, LOF, PE and the high Q values. Further, the high residual values obtained in case
Pred. 1.11 1.11 1.16 1.18 1.18 1.24 1.13 1.24 1.28 1.20 1.27 1.16 1.26 1.33 1.23 1.79 1.63 1.47 1.29 1.41 1.57 1.73 1.05 0.91 0.90 0.86 1.01 0.91 1.50 1.36 1.21 1.28 1.11 0.97 0.86 1.05 1.25 1.11 0.96 1.05 1.09 1.00 1.16 1.10 1.18
pMICca Res.
Obs.
Pred.
0.10 − 0.08 0.01 − 0.06 − 0.18 0.10 0.05 0.16 − 0.16 − 0.01 0.01 0.33 − 0.10 0.01 − 0.15 − 1.15 − 0.02 0.50 − 0.49 0.62 0.37 − 0.76 0.71 − 0.03 -0.01 0.04 0.15 − 0.02 0.45 0.62 0.80 − 0.48 0.04 − 0.11 0.93 − 0.17 0.15 − 0.29 1.15 − 0.20 − 0.26 − 0.15 − 0.35 0.33 − 0.04
1.39 1.27 1.15 1.54 1.19 1.58 1.43 1.35 1.3 1.17 1.67 1.49 1.32 1.58 1.19 0.64 1.31 0.76 0.8 1.13 1.64 0.97 0.86 1.18 1.79 1.8 1.76 1.49 1.65 1.38 1.41 1.1 1.15 1.47 1.19 1.48 1.4 1.12 1.21 0.85 1.44 1.45 1.71 1.43 1.74
1.48 1.40 1.41 1.42 1.40 1.53 1.44 1.45 1.48 1.44 1.50 1.42 1.42 1.45 1.42 1.12 1.13 1.16 1.20 1.16 1.16 1.13 1.31 1.31 1.43 1.41 1.31 1.38 1.30 1.30 1.38 1.37 1.30 1.30 1.38 1.37 1.28 1.28 1.38 1.35 1.38 1.34 1.36 1.31 1.36
Res. − 0.09 − 0.13 − 0.26 0.12 − 0.21 0.05 − 0.01 − 0.10 − 0.18 − 0.27 0.17 0.07 − 0.10 0.13 − 0.23 − 0.48 0.18 − 0.40 − 0.40 − 0.03 0.48 − 0.16 − 0.45 − 0.13 0.36 0.39 0.45 0.11 0.35 0.08 0.03 − 0.27 − 0.15 0.17 − 0.19 0.11 0.12 − 0.16 − 0.17 − 0.50 0.06 0.11 0.35 0.12 0.38
of compounds removed as outliers also supported their removal prior to QSAR model development. Generally for QSAR studies, the biological activities of compounds should span 2–3 orders of magnitude. But in the present study the range of antimicrobial activities of the synthesized compounds is within one order of magnitude. This is similar to the results obtained by Bajaj et al. [10] who stated that the reliability of the QSAR model lies in its predictive ability even though the activity data are in the narrow range. The low residual values observed in ● ▶ Table 3 justify the QSAR studies with the synthesized benzimidazole derivatives. The results obtained from developed QSAR models [Eqs. 1–5] indicated that the antimicrobial activity of benzimidazole derivatives against E. coli, S. aureus and C. albicans was governed by WAP, Mlog P and UI respectively. Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
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Comp.
230 Original Article
▼
Molecular descriptors like WAP [11], 1xsol [12], BAC [13] were calculated for each compound of the dataset (1–45) using DRAGON 6.0 software [8]. In order to develop quantitative model for the prediction of antimicrobial activity of 45 benzimidazole derivatives against Escherichia coli (E. coli), Staphylococcus aureus (S. aureus) and Candida albicans (C. albicans) MLR analysis was used in order to get best QSAR model. The predictive power of the developed QSAR models was validated by leave one out (LOO) cross validation method [14], where a model is built with N–1 compounds and Nth compound is predicted. Each compound is left out of the model derivation and predicted in turn. An indication of the performance is obtained from cross-validated r2 method which is defined as q2 = 1 – Σ(Ypredicted – Yactual)2/Σ(Yactual – Ymean)2 where, Ypredicted, Yactual and Ymean are predicted, actual and mean values of target property (pMIC) respectively. Σ(Ypredicted – Yactual)2 is predictive residual error sum of squares. The validity of developed QSAR models was supported by some other statistical parameters [15] like probable error of the coefficient of correlation (PE), least square error (LSE), Friedman’s lack of fit measure (LOF), standard error of prediction (SEP) and quality value (Q) which were calculated using following formulas: PE = 2(1 − r2)/3√n Where, r is the correlation coefficient and n is the number of compounds used. LSE = ∑ (Yobs − Ycalc)2 Where Yobs and Ycalc are the observed and calculated values. LOF = LSE/{1 − (C + d × p/n)}2 Where LSE is the least square error; C, is the number of descriptors; p, is the number of independent parameters; n is the number of compounds used; d, is the smoothing parameter which controls the bias in the scoring factor between equations with different number of terms and was kept as 1.0. SEP = √LSE/n The predictive ability of MLR models was also quantified in terms of q2, which is defined as: q2 = 1 − {∑ (Yobs − Ycalc)2/(Yobs − Ymean)2} The quality value, Q is given by, Q = r/Se, where Q is the quality value; r is the correlation coefficient and Se is the standard error of estimation. The low value of PE, LSE, LOF and SEP and the high value of Q and q2 are the essential criteria for qualifying the model as the best one. Variation inflation factor [16] is employed to determine the multicolinearity between the physicochemical parameters. The VIF value is calculated as: VIF = 1/1 − r2 Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
Where, r2 is the squared multiple correlation coefficient of one parameter’s effect on the remaining parameters. VIF value greater than 5 indicates the presence of unacceptably large multicolinearity between the parameters in the correlation.
Conclusion
▼
In conclusion, the QSAR study throw highlights on correlation of antimicrobial activity of benzimidazole derivatives with their physicochemical parameters. The predictive power of the developed QSAR models were validated by determination of crossvalidated r2 (q2) using leave one out (LOO) method in addition to other statistical parameters like probable error of the coefficient of correlation (PE), least square error (LSE), Friedman’s lack of fit measure (LOF), standard error of prediction (SEP) and quality value (Q), which supported the validity of the developed QSAR models. The QSAR model developed indicated the importance of WAP, Mlog P and UI in describing the antimicrobial activity.
Conflict of Interest
▼
The authors declare no conflicts of interest.
References
1 Akbas E, Berber I, Sener A et al. Synthesis and antibacterial activity of 4-benzoyl-1-methyl-5-phenyl-1 H-pyrazole-3-carboxylic acid and derivatives. Il Pharmaco 2005; 60: 23–26 2 Goker H, Alp M, Yildiz S. Synthesis and potent antimicrobial activity of some novel N-(alkyl)-2-phenyl-1H-benzimidazole-5-carboxamidines. Molecules 2005; 10: 1377–1386 3 Boiani M, Gonzalez M. Imidazole and benzimidazole derivatives as chemotherapeutic agents. Mini Rev Med Chem 2005; 5: 409–424 4 Podunavac-Kuzmanovic SO, Cvetkovic DD, Barna DJ. QSAR analysis of 2-amino or 2-methyl-1-substituted benzimidazoles against Pseudomonas aeruginosa. Int J Mol Sci 2009; 10: 1670–1682 5 Kumar R, Kumar P, Kumar M et al. Synthesis, antimicrobial evaluation, and QSAR studies of 4-amino-3-hydroxy-naphthalene-1-sulfonic acid derivatives. Med Chem Res 2012; 21: 4301–4310 6 Selvam P, Radhika PP, Janagaraj S et al. Synthesis of novel 2-substituted benzimidazole derivatives as potential antimicrobial agents. Res Biotechnol 2011; 2: 50–57 7 Tuncbilek M, Kiper T, Altanlar N. Synthesis and in vitro antimicrobial activity of some novel substituted benzimidazole derivatives having potent activity against MRSA. Eur J Med Chem 2009; 44: 1024–1033 8 Todeschini R, Viviana C. Molecular descriptors for cheminformatics. 2011; Volume 1. Alphabetical listing., Volume 2. Appendices, References. (Wiley VCH-2009) Talete srl, DRAGON (Software for Molecular Descriptor Calculation) Version 6.0-2011- http://www.talete.mi.it/ 9 Golbraikh A, Tropsha A. Beware of q2. J Mol Graph Model 2002; 20: 269–276 10 Bajaj S, Sambi SS, Madan AK. Prediction of anti-inflammatory activity of N-arylanthranilic acids: computational approach using refined Zagreb Indices. Croat Chem Acta 2005; 78: 165–174 11 Dobrynin AA, Gutman I, Klavzar S et al. Wiener index of hexagonal systems. Acta Appl Math 2002; 72: 247–294 12 Fatemi MH, Malekzadeh H, Shamseddin H. Prediction of supercritical fluid chromatographic retention factors at different percents of organic modifiers in mobile phase. J Sep Sci 2009; 32: 653–659 13 Hosoya H. Chemical meaning of octane number analyzed by topological indices. Croat Chem Acta 2002; 75: 433–445 14 Agrawal VK, Singh J, Mishra KC et al. QSAR study on 5,6-dihydro-2pyrones as HIV-1 protease inhibitors. ARKIVOC 2006; ii: 162–177 15 Mandloi D, Joshi S, Khadikar PV et al. QSAR study on the antibacterial activity of some sulfa drugs: building blockers of Mannich bases. Bioorg Med Chem Lett 2005; 15: 405–411 16 Kumar PM, Karthikeyan C, Moorthy NSH et al. Quantitative structure– activity relationships of selective antagonists of glucagon receptor using QSAR descriptors. Chem Pharm Bull 2008; 54: 1586–1591
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Experimental
225
Development of QSAR for Antimicrobial Activity of Substituted Benzimidazoles
Authors
N. Vashist1, S. S. Sambi1, P. Kumar2, B. Narasimhan2
Affiliations
1
2
Key words ▶ Benzimidazoles ● ▶ Antimicrobial activity ● ▶ QSAR ●
Abstract
▼
QSAR analysis has been done to correlate antimicrobial activity of substituted benzimidazole derivatives with their physicochemical parameters. Developed QSAR models have been cross validated using leave one out (LOO) method. Statistical parameters like probable error of
Introduction
▼
received 30.10.2013 accepted 07.11.2013 Bibliography DOI http://dx.doi.org/ 10.1055/s-0034-1371828 Published online: January 21, 2015 Drug Res 2015; 65: 225–230 © Georg Thieme Verlag KG Stuttgart · New York ISSN 2194-9379 Correspondence Dr. B. Narasimhan Faculty of Pharmaceutical Sciences Maharshi Dayanand University Delhi Road Rohtak-124001 India Tel.: + 91/941/6649 342 Fax: + 91/1262/274 133 [email protected]
In recent years, a number of life-threatening infections caused by multi-drug resistant Gram-positive and Gram-negative pathogenic bacteria have reached an alarming level in many countries. Infections caused by these microorganisms pose a serious challenge to the medical community to develop an effective therapy by developing novel antibacterial agents [1]. The benzimidazole moiety is an important pharmacophore in medicinal chemistry. Diverse biological activities and clinical applications such as antimicrobial [2], anticancer [3] activities have been reported for these derivatives. Quantitative Structure Activity Relationship (QSAR) has proved to be a useful tool for rational search of bioactive molecules. This eliminates unnecessary synthesis of many structures even without testing those [4]. Our research work devoted to rational drug design [5] established the importance of this analytical approach. Hence, in the present study, we hereby report the QSAR studies for substituted benzimidazoles reported by Selvam et al. and Tuncbilek et al. [6, 7].
Results and Discussion
▼
The present study was designed to develop quantitative model to predict the correlation between the antimicrobial activity of a dataset of 45 benzimidazole derivatives against E. coli, S. aureus and ▶ Table 1) and the structural descripC. albicans ( ●
the coefficient of correlation (PE), least square error (LSE), Friedman’s lack of fit measure (LOF), standard error of prediction (SEP) and quality value (Q) were also used to cross validate the models. QSAR studies established the importance of WAP, Mlog P and UI in describing the antimicrobial activities of substituted benzimidazole derivatives.
tors using MLR analysis. Numerical values of various descriptors calculated by Dragon software programme [8] are given in ● ▶ Table 2. Out of these 45 derivatives, some of the compounds having activity against E. coli (1, 2, 4, 10, 12, 28, 33, 36–39, 42 and 45), S. aureus (16, 18– 23, 29–32, 34, 35, 38, 39, 41 and 43), and C. albicans (3, 5, 10, 15, 16, 18, 19, 21, 23, 25–27, 29, 32, 40, 43 and 45) were identified as outliers and removed before the development of best QSAR models as per results of our previous studies [5]. QSAR model for explaining antimicrobial activity of benzimidazole derivatives against E. coli (Eq. 1) was developed using WAP.
QSAR model for antibacterial activity of benzimidazole derivatives against E. coli pMICec = 0.0000146 WAP + 0.669
(1)
n = 31, r = 0.964, r2 = 0.929, Se = 0.0626, q2 = 0.929, F = 379.029, PE = 0.0085, LSE = 0.114, LOF = 0.130, SEP = 0.011, VIF = 0.071, Q = 15.30 Here and thereafter, n is the number of data points, r is the correlation coefficient; r2 is the squared correlation coefficient, Se is the standard error of the estimate; q2 is the cross validated r2 which is obtained by leave one out (LOO) method, F, is the Fischer ratio, PE is probable error of the coefficient of correlation, LSE is least square error, LOF is Friedman’s lack of fit measure, SEP is standard error of prediction, VIF is the variation inflation factor and Q is the quality value.
Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
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University School of Chemical Technology, Guru Gobind Singh Indraprastha University, New Delhi, India Faculty of Pharmaceutical Sciences, Maharshi Dayanand University, Rohtak, India
226 Original Article
Table 1 Antimicrobial activity of benzimidazole derivatives. N H
Comp.
R
1
NO
2
Cl
3
Comp.
OCH
R
6
NO
7
Cl
8
Comp.
OCH
R
11
NO
12
Cl
13
OCH
R
N
pMICec
pMICsa
pMICca
Comp.
1.256
1.212
1.388
4
1.375
1.030
1.266
5
1.153
1.173
1.153
pMICec
pMICsa
pMICca
Comp.
1.446
1.343
1.581
9
1.120
1.180
1.435
10
1.284
1.402
1.351
pMICec
pMICsa
pMICca
1.415
1.277
1.665
14
1.529
1.494
1.494
15
1.325
1.157
1.325
R4
Comp.
R
CH
R
CH
R
CH
pMICec
pMICsa
pMICca
1.305
1.121
1.536
1.016
1.002
1.192
pMICec
pMICsa
pMICca
1.344
1.118
1.301
1.509
1.191
1.174
pMICec
pMICsa
pMICca
1.666
1.342
1.579
1.264
1.081
1.188
Comp.
R1
R2
R3
pMICec
pMICsa
pMICca
16
Cl
H
H
0.645
0.645
0.645
17
Cl
Cl
H
0.708
1.611
1.310
18
Cl
Cl
Cl
0.763
1.968
0.763
19
Cl
Cl
NHCH(CH3)2
0.796
0.796
0.796
20
Cl
Cl
Br
0.825
2.030
1.126
21
Cl
Cl
NH2
0.733
1.937
1.636
22
Cl
H
NH2
0.673
0.974
0.974
23
Cl
OC2H5
0.856
1.759
0.856
0.875
0.875
1.176
0.887
0.887
1.791
F
24
Cl
OC2H5 Cl
25
Cl
OC2H5
NO
Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
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N
Original Article
227
Table 1 Antimicrobial Continued. activity of benzimidazole derivatives. Comp.
R1
R2
26
Cl
OC2H5
27
Cl
Cl
R3
R4
pMICec
pMICsa
pMICca
0.902
0.902
1.805
0.859
1.160
1.762
1.192
0.891
1.493
H
0.750
1.955
1.653
H
0.775
1.979
1.377
OCOCH
OCH
28
Cl
Cl OCOCH
29
Cl
Cl
30
Cl
Cl
31
Cl
Cl
H
0.805
2.010
1.407
32
Cl
Cl
H
0.797
0.797
1.098
33
Cl
Cl
1.145
1.145
1.145
0.864
0.864
1.466
F
Cl
34
Cl
Cl
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F
Cl
35
Cl
Cl
0.889
1.792
1.190
36
Cl
Cl
0.882
0.882
1.484
37
Cl
H
1.100
1.401
1.401
1.122
0.821
1.122
F
38
Cl
H Cl
39
Cl
H
0.906
2.111
1.207
40
Cl
H
0.851
0.851
0.851
41
Cl
H
0.835
0.835
1.437
42
Cl
H
1.150
0.849
1.451
43
Cl
H
0.809
0.809
1.712
0.832
1.434
1.434
0.841
1.142
1.744
OCOCH
NO
CN
44
Cl
H N(CH )
45
Cl
H
The developed QSAR model (Eq. 1) was cross validated by q2 value obtained by leave one out (LOO) method. The higher value of q2 (0.929) indicated that the model developed is a valid one. As the observed and predicted values are close to each other ▶ Table 3), the QSAR model for antibacterial activity against ( ● E. coli (Eq. 1) is a valid one [9]. The validity of the developed QSAR model was also supported by other statistical parameters such as low value of LSE, LOF, PE and the high Q values favours the validity of developed QSAR model (Eq. 1).
QSAR model for antibacterial activity of benzimidazole derivatives against S. aureus
Mlog P was found to be the most important descriptor for explaining the antibacterial activity of benzimidazole derivatives against S. aureus. pMICsa = − 0.114 Mlog P + 1.666
(2)
n = 28, r = 0.364, r2 = 0.132, Se = 0.200, q2 = 0.133, F = 3.969, PE = 0.109, LSE = 0.509, LOF = 0.862, SEP = 0.025, VIF = 0.868, Q = 1.82 Coupling of Mlog P with WAP and 1χsol lead to best MLR model against S. aureus having improved r (from 0.364 to 0.751) and q2 (from 0.132 to 0.564) values (Eq. 3). Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
228 Original Article
Comp.
ZM1
ZM2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
138.00 128.00 132.00 138.00 128.00 168.00 158.00 162.00 168.00 158.00 166.00 156.00 160.00 166.00 156.00 82.00 88.00 94.00 108.00 94.00 94.00 88.00 136.00 136.00 146.00 150.00 132.00 142.00 98.00 98.00 116.00 118.00 128.00 128.00 146.00 148.00 122.00 122.00 158.00 136.00 132.00 140.00 126.00 132.00 142.00
161.00 149.00 154.00 162.00 149.00 205.00 193.00 198.00 206.00 193.00 200.00 188.00 193.00 201.00 188.00 98.00 106.00 114.00 129.00 114.00 114.00 106.00 164.00 164.00 176.00 179.00 160.00 170.00 116.00 116.00 137.00 143.00 155.00 155.00 176.00 182.00 147.00 147.00 188.00 162.00 159.00 168.00 152.00 159.00 174.00
WAP 21 302.00 16 846.00 19 073.00 21 168.00 16 846.00 48 084.00 38 472.00 43 277.00 47 794.00 38 472.00 49 524.00 39 624.00 44 573.00 49 234.00 39 624.00 3 078.00 3 584.00 4 030.00 5 697.00 4 030.00 4 030.00 3 496.00 14 350.00 14 350.00 17 954.00 20 069.00 13 530.00 16 984.00 5 200.00 5 200.00 7 765.00 14 308.00 11 945.00 11 945.00 16 706.00 28 655.00 10 923.00 10 923.00 34 334.00 15 658.00 13 903.00 15 396.00 12 412.00 13 903.00 26 625.00
BAC 6.00 2.00 3.00 6.00 2.00 18.00 10.00 11.00 18.00 10.00 11.00 5.00 6.00 11.00 5.00 2.00 5.00 10.00 19.00 10.00 10.00 5.00 12.00 12.00 22.00 25.00 11.00 19.00 10.00 10.00 27.00 5.00 10.00 10.00 27.00 5.00 5.00 5.00 2.00 12.00 11.00 18.00 6.00 11.00 2.00
χ
1 v
χ
0χsol
1 sol
12.69 11.78 12.31 12.73 11.78 14.53 13.61 14.15 14.56 13.61 14.60 13.69 14.23 14.64 13.69 7.34 7.75 8.16 9.56 8.16 8.16 7.75 12.17 12.17 13.08 13.56 11.67 12.53 8.63 8.63 9.84 10.22 11.13 11.13 12.34 12.72 10.72 10.72 14.28 12.11 11.63 11.93 11.26 11.63 12.31
1
8.03 8.01 8.05 8.19 7.94 9.73 9.71 9.76 9.90 9.64 10.38 10.36 10.41 10.55 10.29 5.84 6.33 6.83 7.95 7.24 6.55 6.06 9.15 9.53 9.55 10.07 8.94 9.44 6.00 6.37 7.56 7.31 8.52 8.90 10.08 9.83 8.03 8.41 10.60 8.96 8.43 9.60 8.32 8.96 9.35
17.93 16.86 17.06 17.93 16.36 21.33 20.25 20.46 21.33 19.75 21.02 19.94 20.15 21.02 19.44 10.75 12.12 13.49 15.28 13.99 12.99 11.62 17.02 18.39 19.47 20.17 17.68 19.26 12.83 14.20 16.20 15.40 16.10 17.47 19.47 18.67 14.73 16.10 20.13 17.89 17.18 18.10 16.31 17.18 17.30
12.69 12.07 12.31 12.73 11.78 14.81 14.19 14.44 14.85 13.90 15.05 14.43 14.68 15.09 14.14 7.63 8.33 9.03 10.14 9.32 8.74 8.04 12.06 12.75 13.37 13.85 12.25 13.10 8.82 9.50 10.42 10.80 11.32 12.00 12.92 13.30 10.62 11.30 14.57 12.40 11.92 12.22 11.55 11.92 12.60
MLR QSAR model for antibacterial activity of benzimidazole derivatives against S. aureus
pMICsa = 0.0000212 WAP – 0.0667 Mlog P – 0.194 1χsol + 3.414 (3) n = 28, r = 0.751, r2 = 0.564, Se = 0.148, q2 = 0.564, F = 10.354, PE = 0.055, LSE = 0.509, LOF = 1.558, SEP = 0.025, VIF = 0.436, Q = 5.074 The higher value of q2 (0.564) indicated that the model developed is a valid one. Validity of the model also supported by the observed and predicted values of benzimidazole derivatives that ▶ Table 3). were found close to each other ( ●
Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
χ
UI 3.91 3.70 3.70 3.70 3.70 3.91 3.70 3.70 3.70 3.70 3.91 3.70 3.70 3.70 3.70 2.59 2.59 2.59 2.59 2.59 2.59 2.59 3.17 3.17 3.46 3.32 3.17 3.32 3.17 3.17 3.17 3.52 3.17 3.17 3.17 3.52 3.17 3.17 3.59 3.32 3.46 3.17 3.46 3.17 3.52
AMR
MlOGP
100.23 97.71 99.37 101.06 97.95 111.77 109.25 110.91 112.61 109.49 115.05 112.53 114.18 115.88 112.76 61.08 65.89 70.91 84.72 73.51 70.06 65.26 97.12 101.71 104.23 108.04 96.96 101.63 69.41 74.00 87.86 85.64 90.72 95.31 109.17 106.95 85.91 90.50 116.77 96.83 93.02 104.36 91.43 100.12 102.15
4.36 4.85 4.04 3.26 4.58 4.78 5.21 4.42 3.92 4.94 4.06 4.49 3.70 2.93 4.22 3.11 3.64 4.16 4.22 4.29 3.48 2.95 4.87 4.98 4.49 4.33 4.76 4.91 4.70 4.82 5.27 5.12 5.48 5.60 5.97 5.82 4.99 5.10 5.32 4.42 4.54 5.49 4.19 4.49 5.34
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Table 2 Values of selected molecular descriptors used in MLR analysis.
QSAR model for antifungal activity of benzimidazole derivatives against C. albicans
QSAR model for explaining antimicrobial activity of benzimidazole derivatives against C. albicans (Eq. 4) was developed using UI. pMICca = 0.0254 UI + 0.504
(4)
n = 28, r = 0.601, r2 = 0.362, Se = 0.133, q2 = 0.362, F = 14.735, PE = 0.080, LSE = 0.438, LOF = 0.508, SEP = 0.024, VIF = 0.638, Q = 2.721 In search of a better QSAR model for explaining antifungal activity of benzimidazole derivatives against C. albicans, we coupled UI with BAC, resulted in the best QSAR model (Eq. 5) having improved r and q2 values.
Original Article
229
Table 3 Comparison of observed verses predicted antimicrobial activity of benzimidazole derivatives using best MLR models.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
pMICsa
pMICec Obs.
Pred.
1.26 1.37 1.15 1.31 1.02 1.45 1.12 1.28 1.34 1.51 1.42 1.53 1.32 1.67 1.26 0.64 0.71 0.76 0.8 0.82 0.73 0.67 0.86 0.88 0.89 0.9 0.86 1.19 0.75 0.77 0.81 0.8 1.15 0.86 0.89 0.88 1.1 1.12 0.91 0.85 0.83 1.15 0.81 0.83 0.84
0.98 0.91 0.95 0.98 0.91 1.37 1.23 1.30 1.37 1.23 1.39 1.25 1.32 1.39 1.25 0.71 0.72 0.73 0.75 0.73 0.73 0.72 0.88 0.88 0.93 0.96 0.87 0.92 0.74 0.74 0.78 0.88 0.84 0.84 0.91 1.09 0.83 0.83 1.17 0.90 0.87 0.89 0.85 0.87 1.06
pMICca = 0.00456 BAC + 0.257 UI + 0.444
Res.
Obs.
0.28 0.46 0.20 0.33 0.11 0.08 − 0.11 − 0.02 − 0.03 0.28 0.03 0.28 0.00 0.28 0.01 − 0.07 − 0.01 0.03 0.05 0.09 0.00 − 0.05 − 0.02 0.00 − 0.04 − 0.06 − 0.01 0.27 0.01 0.03 0.03 − 0.08 0.31 0.02 − 0.02 − 0.21 0.27 0.29 − 0.26 − 0.05 − 0.04 0.26 − 0.04 − 0.04 − 0.22
1.21 1.03 1.17 1.12 1 1.34 1.18 1.4 1.12 1.19 1.28 1.49 1.16 1.34 1.08 0.64 1.61 1.97 0.8 2.03 1.94 0.97 1.76 0.88 0.89 0.9 1.16 0.89 1.95 1.98 2.01 0.8 1.15 0.86 1.79 0.88 1.4 0.82 2.11 0.85 0.83 0.85 0.81 1.43 1.14
(5)
n = 28, r = 0.629, r2 = 0.396, Se = 0.132, q2 = 0.393, F = 8.184, PE = 0.076, LSE = 0.438, LOF = 0.709, SEP = 0. 024, VIF = 0. 604, Q = 4.765 The developed QSAR model (Eq. 5) was cross validated by q2 value obtained by leave one out (LOO) method. The low value of q2 (0.396) indicated that the model developed is an invalid one. But according to the recommendations of Golbraikh and Tropsha, as the observed and predicted values are close to each other ▶ Table 3), the QSAR model for antifungal activity against C. ( ● albicans (Eq. 5) is a valid one [9]. The validity of the developed QSAR model was also supported by the low LSE, LOF, PE and the high Q values. Further, the high residual values obtained in case
Pred. 1.11 1.11 1.16 1.18 1.18 1.24 1.13 1.24 1.28 1.20 1.27 1.16 1.26 1.33 1.23 1.79 1.63 1.47 1.29 1.41 1.57 1.73 1.05 0.91 0.90 0.86 1.01 0.91 1.50 1.36 1.21 1.28 1.11 0.97 0.86 1.05 1.25 1.11 0.96 1.05 1.09 1.00 1.16 1.10 1.18
pMICca Res.
Obs.
Pred.
0.10 − 0.08 0.01 − 0.06 − 0.18 0.10 0.05 0.16 − 0.16 − 0.01 0.01 0.33 − 0.10 0.01 − 0.15 − 1.15 − 0.02 0.50 − 0.49 0.62 0.37 − 0.76 0.71 − 0.03 -0.01 0.04 0.15 − 0.02 0.45 0.62 0.80 − 0.48 0.04 − 0.11 0.93 − 0.17 0.15 − 0.29 1.15 − 0.20 − 0.26 − 0.15 − 0.35 0.33 − 0.04
1.39 1.27 1.15 1.54 1.19 1.58 1.43 1.35 1.3 1.17 1.67 1.49 1.32 1.58 1.19 0.64 1.31 0.76 0.8 1.13 1.64 0.97 0.86 1.18 1.79 1.8 1.76 1.49 1.65 1.38 1.41 1.1 1.15 1.47 1.19 1.48 1.4 1.12 1.21 0.85 1.44 1.45 1.71 1.43 1.74
1.48 1.40 1.41 1.42 1.40 1.53 1.44 1.45 1.48 1.44 1.50 1.42 1.42 1.45 1.42 1.12 1.13 1.16 1.20 1.16 1.16 1.13 1.31 1.31 1.43 1.41 1.31 1.38 1.30 1.30 1.38 1.37 1.30 1.30 1.38 1.37 1.28 1.28 1.38 1.35 1.38 1.34 1.36 1.31 1.36
Res. − 0.09 − 0.13 − 0.26 0.12 − 0.21 0.05 − 0.01 − 0.10 − 0.18 − 0.27 0.17 0.07 − 0.10 0.13 − 0.23 − 0.48 0.18 − 0.40 − 0.40 − 0.03 0.48 − 0.16 − 0.45 − 0.13 0.36 0.39 0.45 0.11 0.35 0.08 0.03 − 0.27 − 0.15 0.17 − 0.19 0.11 0.12 − 0.16 − 0.17 − 0.50 0.06 0.11 0.35 0.12 0.38
of compounds removed as outliers also supported their removal prior to QSAR model development. Generally for QSAR studies, the biological activities of compounds should span 2–3 orders of magnitude. But in the present study the range of antimicrobial activities of the synthesized compounds is within one order of magnitude. This is similar to the results obtained by Bajaj et al. [10] who stated that the reliability of the QSAR model lies in its predictive ability even though the activity data are in the narrow range. The low residual values observed in ● ▶ Table 3 justify the QSAR studies with the synthesized benzimidazole derivatives. The results obtained from developed QSAR models [Eqs. 1–5] indicated that the antimicrobial activity of benzimidazole derivatives against E. coli, S. aureus and C. albicans was governed by WAP, Mlog P and UI respectively. Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
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Comp.
230 Original Article
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Molecular descriptors like WAP [11], 1xsol [12], BAC [13] were calculated for each compound of the dataset (1–45) using DRAGON 6.0 software [8]. In order to develop quantitative model for the prediction of antimicrobial activity of 45 benzimidazole derivatives against Escherichia coli (E. coli), Staphylococcus aureus (S. aureus) and Candida albicans (C. albicans) MLR analysis was used in order to get best QSAR model. The predictive power of the developed QSAR models was validated by leave one out (LOO) cross validation method [14], where a model is built with N–1 compounds and Nth compound is predicted. Each compound is left out of the model derivation and predicted in turn. An indication of the performance is obtained from cross-validated r2 method which is defined as q2 = 1 – Σ(Ypredicted – Yactual)2/Σ(Yactual – Ymean)2 where, Ypredicted, Yactual and Ymean are predicted, actual and mean values of target property (pMIC) respectively. Σ(Ypredicted – Yactual)2 is predictive residual error sum of squares. The validity of developed QSAR models was supported by some other statistical parameters [15] like probable error of the coefficient of correlation (PE), least square error (LSE), Friedman’s lack of fit measure (LOF), standard error of prediction (SEP) and quality value (Q) which were calculated using following formulas: PE = 2(1 − r2)/3√n Where, r is the correlation coefficient and n is the number of compounds used. LSE = ∑ (Yobs − Ycalc)2 Where Yobs and Ycalc are the observed and calculated values. LOF = LSE/{1 − (C + d × p/n)}2 Where LSE is the least square error; C, is the number of descriptors; p, is the number of independent parameters; n is the number of compounds used; d, is the smoothing parameter which controls the bias in the scoring factor between equations with different number of terms and was kept as 1.0. SEP = √LSE/n The predictive ability of MLR models was also quantified in terms of q2, which is defined as: q2 = 1 − {∑ (Yobs − Ycalc)2/(Yobs − Ymean)2} The quality value, Q is given by, Q = r/Se, where Q is the quality value; r is the correlation coefficient and Se is the standard error of estimation. The low value of PE, LSE, LOF and SEP and the high value of Q and q2 are the essential criteria for qualifying the model as the best one. Variation inflation factor [16] is employed to determine the multicolinearity between the physicochemical parameters. The VIF value is calculated as: VIF = 1/1 − r2 Vashist N et al. QSAR Studies of Benzimidazoles … Drug Res 2015; 65: 225–230
Where, r2 is the squared multiple correlation coefficient of one parameter’s effect on the remaining parameters. VIF value greater than 5 indicates the presence of unacceptably large multicolinearity between the parameters in the correlation.
Conclusion
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In conclusion, the QSAR study throw highlights on correlation of antimicrobial activity of benzimidazole derivatives with their physicochemical parameters. The predictive power of the developed QSAR models were validated by determination of crossvalidated r2 (q2) using leave one out (LOO) method in addition to other statistical parameters like probable error of the coefficient of correlation (PE), least square error (LSE), Friedman’s lack of fit measure (LOF), standard error of prediction (SEP) and quality value (Q), which supported the validity of the developed QSAR models. The QSAR model developed indicated the importance of WAP, Mlog P and UI in describing the antimicrobial activity.
Conflict of Interest
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The authors declare no conflicts of interest.
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